On the Distributions of the State Sizes of Discrete Time Homogeneous Markov Systems
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The evolution of a closed discrete-time homogeneous Markov system (HMS) is determined by the evolution of its state sizes in time. In order to examine the variability of the state sizes, their moments are evaluated for any time point, and recursive formulae for their computation are derived. As a consequence the asymptotic values of the moments for a convergent HMS can be evaluated. The respective recursive formula for a HMS with periodic transition matrix is given. The p.d.f.’s of the state sizes follow directly by means of the moments. The theoretical results are illustrated by a numerical example.
KeywordsStochastic population systems Discrete-time homogeneous Markov models Markov systems
AMS 2000 Subject ClassificationPrimary 90B70 62E99; Secondary 91D35
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